Virtual Reality Spaces for Visual Data Mining with Multiobjective Evolutionary Optimization: Implicit and Explicit Function Representations Mixing Unsupervised and Supervised Properties

Multi-objective optimization is used for the computation of virtual reality spaces for visual data mining and knowledge discovery. Two methods for computing new spaces are discussed: implicit and explicit function representations. In the first, the images of the objects are computed directly, and in the second, universal function approximators (neural networks) are obtained. The pros and cons of each approach are discussed, as well as their complementary character. The NSGA-II algorithm is used for computing spaces requested to minimize two objectives: a similarity structure loss measure (Sammon´s error) and classification error (mean cross-validation error on a k-nn classifier). Two examples using solutions along approximations to the Pareto front are presented: Alzheimer´s disease gene expressions and geophysical fields for prospecting underground caves. This approach is a general non-linear feature generation and can be used in problems not necessarily oriented to the construction of visual data representations.